Molecular self-diffusion measured with NMR (nuclear magnetic resonance) (Callaghan, 2011 in “Translational Dynamics & Magnetic Resonance” (Oxford, Oxford University Press); Price, 2009 in “NMR Studies of Translational Motion” (Cambridge, Cambridge University Press)) is used to non-invasively study the morphology of the water-filled pore space of a wide range of materials, e.g., rocks (Hürlimann et al., 1994 “Restricted diffusion in sedimentary rocks. Determination of surface-area-to-volume ratio and surface relaxivity”. J Magn Reson A 111, 169-178), emulsions (Topgaard et al., 2002, “Restricted self-diffusion of water in a highly concentrated W/O emulsion studied using modulated gradient spin-echo NMR”. J Magn Reson 156, 195-201.), and cheese (Mariette et al., 2002, “1H NMR diffusometry study of water in casein dispersions and gels”. J Agric Food Chem 50, 4295-4302.).
Anisotropy of the pore structure renders the water self-diffusion anisotropic, a fact that is utilized for three-dimensional mapping of nerve fiber orientations in the white matter of the brain where the fibers have a preferential direction on macroscopic length scales (Basser et al., 1994, “MR diffusion tensor spectroscopy and imaging”. Biophys J 66, 259-267; Beaulieu, 2002, “The basis of anisotropic water diffusion in the nervous system—a technical review”. NMR Biomed 15, 435-455; Moseley et al., 1991, “Anisotropy in diffusion-weighted MRI”. Magn Reson Med 19, 321-326.). The degree of the macroscopic diffusion anisotropy is often quantified by the non-dimensional fractional anisotropy index (Basser and Pierpaoli, 1996, “Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI”. J Magn Reson B 111, 209-219.).
Also microscopic anisotropy in a globally isotropic material can be detected with diffusion NMR, originally through the characteristic curvature observed in the echo attenuation of conventional single-PGSE (pulsed gradient spin-echo) techniques (Callaghan and Söderman, 1983, in “Examination of the lamellar phase of aerosol OT/water using pulsed field gradient nuclear magnetic resonance”. J Phys Chem 87, 1737-1744; Topgaard and Söderman, 2002, in “Self-diffusion in two- and three-dimensional powders of anisotropic domains: An NMR study of the diffusion of water in cellulose and starch”. J Phys Chem B 106, 11887-11892.) and, more recently, by using double-PGSE approaches in which the NMR signal is encoded for displacements over two separate time periods (Mitra, 1995, in “Multiple wave-vector extension of the NMR pulsed-field-gradient spin-echo diffusion measurement”. Phys Rev B 51, 15074-15078.). The presence of microscopic anisotropy can be inferred by comparing echo attenuation data obtained with collinear and orthogonal displacement encoding (Callaghan and Komlosh, 2002, in “Locally anisotropic motion in a macroscopically isotropic system: displacement correlations measured using double pulsed gradient spin-echo NMR”. Magn Reson Chem 40, S15-S19.; Komlosh et al., 2007, in “Detection of microscopic anisotropy in gray matter and in novel tissue phantom using double Pulsed Gradient Spin Echo MR”. J Magn Reson 189, 38-45.; Komlosh et al., 2008, in “Observation of microscopic diffusion anisotropy in the spinal cord using double-pulsed gradient spin echo MRI”. Magn Reson Med 59, 803-809.), by the characteristic signal modulations observed when varying the angle between the directions of displacement encoding (Mitra, 1995, in “Multiple wave-vector extension of the NMR pulsed-field-gradient spin-echo diffusion measurement”. Phys Rev B 51, 15074-15078.; Shemesh et al., 2011, in “Probing Microscopic Architecture of Opaque Heterogeneous Systems Using Double-Pulsed-Field-Gradient NMR”. J Am Chem Soc 133, 6028-6035, and “Microscopic and Compartment Shape Anisotropies in Gray and White Matter Revealed by Angular Bipolar Double-PFG MR”. Magn Reson Med 65, 1216-1227.), or by a two-dimensional correlation approach (Callaghan and Furó, 2004, in “Diffusion-diffusion correlation and exchange as a signature for local order and dynamics”. J Chem Phys 120, 4032-4038; Hubbard et al., 2005, 2006, in “A study of anisotropic water self-diffusion and defects in the lamellar mesophase”. Langmuir 21, 4340-4346, and “Orientational anisotropy in polydomain lamellar phase of a lyotropic liquid crystal”. Langmuir 22, 3999-4003.).
In typical diffusion magnetic resonance imaging (MRI) experiments, only a voxel average anisotropy can be detected. Detection of microscopic anisotropy in a globally isotropic material through the characteristic echo attenuation curve in conventional single-PGSE techniques demands high diffusion weighting, often not feasible in clinical applications, and suffers from very low sensitivity to microscopic anisotropy. Information about microscopic anisotropy is further hindered in such experiments by possible isotropic diffusion contributions to the echo attenuation which are superposed to anisotropic contributions. The low sensitivity to microscopic anisotropy is the main pitfall also in analysis of data from double PGSE experiments.
The present techniques are not adequately sensitive to microscopic anisotropy and are not best suited for clinical applications. Highly sensitive techniques to detect microscopic anisotropy, feasible for clinical applications, are thus needed. Furthermore, there is a need for a robust and fast data analysis approach allowing for an unambiguous quantification of microscopic anisotropy associated with a simple but concise parameter for its quantification. One aim of the present invention is to provide a new analysis method along with the novel parameter, microscopic fractional anisotropy (μFA), providing a robust, fast and highly sensitive means for quantifying microscopic anisotropy, which is suitable in non-clinical and in clinical applications alike.